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A hybrid method of evolutionary algorithm and simple cell mapping for multi-objective optimization problems

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Abstract

A hybrid method is proposed to take advantages of evolutionary algorithms (EAs) and the simple cell mapping (SCM) for multi-objective optimization problems (MOPs). The hybrid method starts with a random search for Pareto optimal solutions with an EA, and follows up with a neighborhood based search and recovery algorithm using the SCM. The non-dominated sorting genetic algorithm-II (NSGA-II) is used as an example of EAs. It is found that the SCM based search and recovery algorithm can reconstruct the branches of the Pareto set even when only one point in the vicinity of the set is available from the random search by the EA. We have chosen several benchmark MOPs to compare NSGA-II and SCM separately with the EA\(+\)SCM hybrid method while using the Hausdorff distance as a performance metric, and applied the method to develop multi-objective optimal designs of PID controls for a nonlinear oscillator with time delay. The results show that the EA\(+\)SCM hybrid method is very promising.

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Acknowledgments

The material in this paper is based on work supported by Grants (11172197, 11332008 and 11572215) from the National Natural Science Foundation of China, and a Grant from the University of California Institute for Mexico and the United States (UC MEXUS) and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT) through the project “Hybridizing Set Oriented Methods and Evolutionary Strategies to Obtain Fast and Reliable Multi-objective Optimization Algorithms”. The third author (FRX) would like to thank China Scholarship Council (CSC) for sponsoring his studies in the United States of America.

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Authors and Affiliations

  1. School of Engineering, University of California at Merced, Merced, CA, 95344, USA

    Yousef Naranjani & Jian-Qiao Sun

  2. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Fu-Rui Xiong

  3. Depto de Computacion, CINVESTAV-IPN, 07360, Mexico City, Mexico

    Carlos Hernández & Oliver Schütze

Authors
  1. Yousef Naranjani
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  2. Carlos Hernández
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  3. Fu-Rui Xiong
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  4. Oliver Schütze
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  5. Jian-Qiao Sun
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Correspondence to Jian-Qiao Sun.

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Jian-Qiao Sun: Honorary Professor of Tianjin University.

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Naranjani, Y., Hernández, C., Xiong, FR. et al. A hybrid method of evolutionary algorithm and simple cell mapping for multi-objective optimization problems. Int. J. Dynam. Control 5, 570–582 (2017). https://doi.org/10.1007/s40435-016-0250-1

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  • DOI: https://doi.org/10.1007/s40435-016-0250-1

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